Only the effect applied by Arcane Shot overcomes non-magical resistance
As per the description given:
Once per turn, when you fire an arrow from a shortbow or longbow as part of the Attack action, you can apply one of your Arcane Shot options to that arrow.
And the options themselves:
Arcane Shot Options
The options are all ...
The penalty from Combat Expertise applies to all attacks for 1 round starting when the standard attack action or full attack action is taken
Because the benefit of the feat Combat Expertise (Player's Handbook 92) applies when the standard attack or full attack action is taken—not, in the latter case, when each iterative attack during the full attack is made—...
Yes, Combat Expertise applies its penalty to all attacks
Well, you are correct that the penalty applies to all attacks:
The changes to attack rolls and Armor Class last until your next action.
(Combat Expertise, footnote mine)
If you have a BAB of +6/−1, and no other bonuses,2 and you use Combat Expertise with a penalty of −3, you would gain +3 AC ...
You need two weapons to perform Two-weapon fighting
The rule is fairly clear on this. From the Basic Rules:
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand.
You need to hold a light melee ...
No, action surge can't be used while surprised in this context
Arcane Charge says:
At 15th level, you gain the ability to teleport up to 30 feet to an unoccupied space you can see when you use your Action Surge
To use an ability, you must do (and thus be able to do) whatever that ability is allowing you to do.
Action Surge says:
Starting at 2nd ...
All Push, no Pull
From my understanding of Pushing Attack, you must move the creature you attacked away from you.
The description of the Battle Master's Pushing Attack maneuver (PHB, p. 74) says:
When you hit a creature with a weapon attack, you can expend one superiority die to attempt to drive the target back. You add the superiority die to the attack'...